A multi-constrained supply chain model with optimal production rate in relation to quality of products under stochastic fuzzy demand

For the production of complex products, this study investigates a flexible production system with a variable production rate as an alternative method to overcome the stock-out risk because of the uncertainty of fuzzy-stochastic demand in an integrated model. The variable production rate enables vendors to fulfill demand uncertainties and reduce the lead time. To establish the relationship between the process quality and production rate three functions, linear, quadratic, and cubic, have been introduced in the mode. The development of such an advanced flexible production system requires a considerably higher setup cost and increases the supply chain cost. To overcome this, the authors introduce a discrete investment function to control setup costs. Authors utilize a crashing cost to reduce the duration of the lead time within the supply chain (SC) structure. In real-life, vendors and buyers face different constraints and set some targets for themselves. Here, the authors consider the storage space and budget constraint for the vendor and customers’ service level constraint for the buyer. An SC model is proposed to find the optimal order quantity, reorder point, lead time, investment for setup cost reduction, and production rate with the minimized total expected cost of the chain. To get the optimal solutions to decision variables, the authors employed a classical optimization technique in the proposed model. An improved algorithm for the global minimum expected cost of SC is designed under the flexible production system. Three numerical examples with comparative study to the previous model and the sensitivity analysis are included to test and validate the proposed model. The numerical analysis and comparative study prove that the proposed model attains the minimum SC cost at the decision variables' optimal values.